There are also systems where a bladder is infalted in the chimney and new mortar is pumped around it.  This Old House used this system on a number of projects.
The concrete injection is very expensive.  
A steel liner is more affordable.
I have thought a lot about the loss of basic skills as being discussed here.  I am "skilled" in many ways--carpenter, good at lots of things--but my "skills" are largely mute absent the grid.  
my "skills" are largely mute absent the grid.

It's "moot".

http://www.thefreedictionary.com/moot

Sorry. I couldn't help it.

Jack